# PharmPK Discussion - Allometry human to rat

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• On 19 Aug 2010 at 13:37:10, rahul vats (rahulvats1983.at.gmail.com) sent the message
`Dear all, I have a query related to calculation of dose. I am working on nano-formulation of a drug which is available as a  tablet form in the market.It's pharmacokintic parameters, in tablet formulation for humans, are: Tmax-    4hrsCmax-   300ng/mlt1/2-       12hrsDose -   150mg (70kg human) Dosing frequency-two times in a day (b.i.d) Now my question is what concentration of the drug in the plasma should  be targeted? Cmax?or C last-Concentration before second dose? Here i do not know EC50 concentration of the drug for targeting the  plasma concentration. Next question is how to scale down the dose to rat as my pharmacokinetic  animal is rat?Regards,Rahul Vats`
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• On 19 Aug 2010 at 17:25:45, (R.ter.Heine.at.meandermc.nl) sent the message
`The following message was posted to: PharmPKRahul,The target concentration to obtain totally depends on the PK-PDrelationship of the drug. If no interspecies scaling has been performedpreviously with your drug, you can calculate the dose assuming a linearrelationship of body weight with V/F and a power relationship (0.75power) with CL/F.Cheers,Rob ter Heine---Rob ter Heine, PhD, PharmDMeander Medical Center, hospital Pharmacy`
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• On 20 Aug 2010 at 08:18:45, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message
`Rahul,> It's pharmacokintic parameters, in tablet formulation for humans, are:>  > Tmax-    4hrs> Cmax-   300ng/ml> t1/2-       12hrs> Dose -   150mg (70kg human)>   From these secondary PK parameters you can make a guess at the  primary PK parameters. With a Tmax of 4 h and Thalf of 12 h the conc extrapolated back to time zero from Cmax (300 ng/mL) could be about 500 ng/mL (and absorption half-life about 1 h). Assuming bioavailability of 100% (for example) the conc after an IV bolus dose would be 500 ng/mL=500 ug/L. Thus the volume of distribution (V) is about 150000 mcg/500 mcg=300 L/70kg and clearance (CL), calculated from V x ln(2)/Thalf, is about 17 L/h/70kg.> Dosing frequency-two times in a day (b.i.d)>  The average steady state conc in humans is ratein/CL=(150mg/12h)/17  L/h which is about 0.7 mg/L or 700 mcg/L.> Now my question is what concentration of the drug in the plasma should  be targeted?>  > Cmax?> or>  > C last-Concentration before second dose?>  The average steady state conc (700 mcg/L) is a first guess at the target concentration. Cmax and Cmin are rarely sensible first choices for the target conc unless you know something special about the pharmacodynamics (e.g. for some antibiotics it is empirically found that being above some magic minimum conc is usually sufficient).> Here i do not know EC50 concentration of the drug for targeting the  plasma concentration.>  If you looked for PKPD info in humans or non-human species you might find an estimate there. But at this first stage of making guesses for suitable doses for the rat I think aiming at the human average steady state conc would get you started. This is the approach that is typically applied (in reverse) when trying to guess human doses from rats.> Next question is how to scale down the dose to rat as my  pharmacokinetic animal is rat?Most of the differences between rats and humans are explained by differences in size (e.g. see Teitelbaum et al. 2010) so a first step is to apply allometric theory (see Holford 1996 for basic concepts and Savage et al. 2008 for the theory and its refinements):Vrat L      = V L/70kg x (WTrat/70kg)^1CLrat L/h = CL L/h/70kg x (WTrat/70kg)^(3/4)There are often quite big differences in PK between species that are not predictable. Allometry cannot predict species differences in V or CL that are not directly associated with size. However, even when other things, such as in vitro enzyme activity in the different species, are taken into account then the predictions are often not much better (see Teitelbaum again). So don't be surprised if the rat PK turns out to be different from these human derived guesses.Best wishes,NickHolford NH. A size standard for pharmacokinetics. Clin Pharmacokinet. 1996;30(5):329-32.Savage VM, Deeds EJ, Fontana W. Sizing up allometric scaling theory. PLoS Comput Biol. 2008;4(9):e1000171.Teitelbaum Z, Lave T, Freijer J, Cohen AF. Risk assessment in extrapolation of pharmacokinetics from preclinical data to humans. Clin Pharmacokinet. 2010;49(9):619-32.`
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• On 20 Aug 2010 at 19:58:02, rahul vats (rahulvats1983.-a-.gmail.com) sent the message
`Dear Sir, Many thanks for your explanation. Still i have one doubt. As you explained how to get an idea about Css average and you suggested  to target this concentration rather than Cmax or Clast. In order to calculate rat dose using allometric  equation  i found a  factor 4 to be multiplied in to the human dose (mg/kg) e.g. if human  dose is 150 mg for 70 kg human (150/70=2.1 mg/kg)So rat dose will be approx. 4*2.1=8.4 mg/kg Will this dose of rat be sufficient to produce Css average (700ng/ml )  concentration in plasma ? or I have to optimize rat dose without applying allometry to produce Css  average concentration as predicted from human will suffices the purpose. Eagerly waiting for your expert comment.Regards, Rahul vats`
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• On 21 Aug 2010 at 08:43:39, Nick Holford (n.holford.at.auckland.ac.nz) sent the message
`Rahul,> In order to calculate rat dose using allometric  equation  i found a  factor 4 to be multiplied in to the human dose (mg/kg) e.g. if human  dose is 150 mg for 70 kg human (150/70=2.1 mg/kg)>> So rat dose will be approx. 4*2.1=8.4 mg/kg>  > Will this dose of rat be sufficient to produce Css average (700ng/ml )  concentration in plasma ? oThe allometric formulas for calculating the rat doses are:Vrat L      = V L/70kg x (WTrat/70kg)^1CLrat L/h = CL L/h/70kg x (WTrat/70kg)^(3/4)I used these and worked out that you must have been using a WTrat of 225 g in order to find a ratio of mg/kg doses of 4 (see table below).The dose of 8.4 mg/kg every 12 h in the rat would be predicted to have an average steady state conc of 700 mcg/L based on allometry and size alone. Note however that the human half-life (12.2 h with these values of CL and V) is 4 times longer than the rat prediction (2.9 h). You should consider more frequent dosing in the rat if you also want to match the peak to trough ratio expected in humans.Good luck!NickWTrat  0.224598   kgWThuman  70   kghuman  V   300   L/70kghuman CL  17   L/h/70kghuman Thalf   12.2   hrat V  0.962562   L/ratrat CL   0.229182   L/h/ratrat Thalf   2.9   htarget conc   700   mcg/Lloading rat   673.7937   mcgmaintenance rat   160.4271   mcg/h  8.57143   mg/kg/12 hmaintenance human   2.142857   mg/kg/12hrat/human   4`
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